The proof of a conjecture on largest Laplacian and signless Laplacian H-eigenvalues of uniform hypergraphs

DOI10.1016/j.laa.2015.10.013zbMath1330.15025arXiv1506.03330OpenAlexW1951456903WikidataQ123143351 ScholiaQ123143351MaRDI QIDQ898785

Xi-Ying Yuan, Liqun Qi, Jia-yu Shao

Publication date: 18 December 2015

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.03330

zbMATH Keywords

uniform hypergraphadjacency tensorsignless Laplacian tensorLaplacian tensorlargest H-eigenvalue

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Inequalities involving eigenvalues and eigenvectors (15A42)

Related Items (15)

The \(H\)-spectra of a class of generalized power hypergraphs ⋮ On the principal eigenvectors of uniform hypergraphs ⋮ Equitable partition theorem of tensors and spectrum of generalized power hypergraphs ⋮ \(\mathrm{P}\)-tensors, \(\mathrm{P}_0\)-tensors, and their applications ⋮ The cyclic index of adjacency tensor of generalized power hypergraphs ⋮ Computing all Laplacian H-eigenvalues for a uniform loose path of length three ⋮ The spectrum of a class of uniform hypergraphs ⋮ On the \(\alpha \)-spectra of uniform hypergraphs and its associated graphs ⋮ On the spectral radius of uniform weighted hypergraph ⋮ On spectral theory of a k-uniform directed hypergraph ⋮ Finding all H-Eigenvalues of Signless Laplacian Tensor for a Uniform Loose Path of Length Three ⋮ Spectral radius of uniform hypergraphs and degree sequences ⋮ The least H-eigenvalue of signless Laplacian of non-odd-bipartite hypergraphs ⋮ Spectral radii of two kinds of uniform hypergraphs ⋮ Some properties on \(\alpha\)-least eigenvalue of uniform hypergraphs and their applications

Cites Work

• Some spectral properties of uniform hypergraphs
• \(H^{+}\)-eigenvalues of Laplacian and signless Laplacian tensors
• The largest Laplacian and signless Laplacian \(H\)-eigenvalues of a uniform hypergraph
• Largest adjacency, signless Laplacian, and Laplacian H-eigenvalues of loose paths
• Perron-Frobenius theorem for nonnegative tensors
• Perron-Frobenius theorem for nonnegative multilinear forms and extensions
• On the spectral radius of a class of non-odd-bipartite even uniform hypergraphs
• A general product of tensors with applications
• Cored hypergraphs, power hypergraphs and their Laplacian H-eigenvalues
• The eigenvectors associated with the zero eigenvalues of the Laplacian and signless Laplacian tensors of a uniform hypergraph
• Further Results for Perron–Frobenius Theorem for Nonnegative Tensors II
• Some spectral properties and characterizations of connected odd-bipartite uniform hypergraphs

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